1. Field of the Invention
This invention relates generally to impedance balanced transmission lines and more particularly to micro or microstrip transmission lines, such as, for example, fabricated in integrated circuits (ICs) or formed on PCBs.
2. Description of the Related Art
The application of high frequency transmission lines in integrated circuits (ICs) or in LSI circuits is known. The characteristic impedance of such transmission lines follows the well known module equation per equation (1) below:Zo=√{square root over ((R+jωL)/(G+jωC))}{square root over ((R+jωL)/(G+jωC))}  (1)
R is series resistance per unit length (Ω/mm or cm), G is the shunt (parallel conductance) Sieman per unit length (S/mm or in cm), L is the line or parallel inductance per unit length (H/mm or cm) and C is the line capacitance per unit length (F/mm or cm) and ωis the operating frequency (2 π times the frequency).
The propagation constant isγ=√{square root over ((R+jωL)(G+jωC)}{square root over ((R+jωL)(G+jωC)}=α+jβ,  (2)                where b is a complex number. The real part, α, is called the attenuation constant and the imaginary part, β, is called the phase constant. The group velocity, Vg is:        
                              V          g                =                              ⅆ            ω                                ⅆ            β                                              (        3        )            
Impedance of a nearly lossless, ideal transmission line is frequency independent when R and G are zero or nearly zero, i.e., R<<jωL and G<<jωC:Zo=√{square root over (L/C)}  (4)
In this case, α is equal to zero and β=ω√{square root over (LC)}, and, therefore, group velocity, Vg, in equation (3) is constant over frequency and the characteristic impedance, Z0, is constant and the transmission line will not be dispersive, that is, there will not be any pulse spreading due to group velocity delay (GVD), since, in reality, the propagation of a signal in the transmission line has a linewidth made up of multiple different frequencies. The dielectric losses are small and the value G in the above equation (1) is typically ignored. Thus, the function in this case is similar to that of just pure passive transmission line resistance resulting in no or little signal dispersion. Therefore, if some control is exercised over transmission line constraints, a uniform group delay for a propagating high frequency signal can be achieved even with a lossy line, at least in principal, except that there will be some skin effect at very high frequencies rendering the line lossy. By choosing RC=GL or, equivalently, choosing the L/R time constant of the series impedance Z equal to the C/G time constant of the shunt resistance Y, the result is that a constant group velocity delay (GVD) in the transmitted signal in the transmission line is achieved at least for frequencies where R and G have little value so that equation (2) holds substantially true. This has also been referred to as the Heaviside relationship, an early investigator of transmission lines in telephony.
In the case of microstrip transmission lines, when the signal frequency is very low, such as in the multiple megahertz or kilohertz frequency range or lower, the series resistance, R, becomes large since ω is going to zero. In such a case, R becomes an important consideration in transmission line design. On the other hand, when the signal frequency is very high, such as in the cases of multiple GHz range, serious skin effect can result in the transmission line resulting high line losses. It has been suggested by those skilled in the art that setting LG=RC is best accomplished by increasing either L or C, rather than by increasing R or G because increasing the series resistance and/or shunt resistance provides an undesirable effect of increased transmission line attenuation. See, as an example, page 124 in the book entitled, “The Design of CMOS Radio-Frequency Integrated Circuits” by Thomas H. Lee, Cambridge University Press, 1998. Most of the traditional microwave transmission line applications are primarily involve with narrow band signals. Therefore, those skilled in the art confine the L and C such that R<<jωL and G<<jωC. However, it is difficult to achieve such a condition with a broadband signal which has frequency components practically down to DC or zero frequency.
More particularly in the case of IC micro transmission lines, when the line frequency becomes low, such as below 2 or 3 GHz, for example, R becomes comparable to jωL or even much larger comparable to jωL. The characteristic impedance in this case becomes a complex number, is not constant, and is frequency dependent. This complex nature and frequency dependency nature of the characteristic impedance causes a propagation group velocity delay (GVD) of the signal traveling along the transmission line and, thus, the line is unacceptably dispersive. This turns out to be a characteristic of the transmission line and has nothing to do with transmission line reflection although reflection will also occur since the transmission line is not impedance matched.
What is needed is to extend the range of frequencies over which a micro transmission line has constant characteristic impedance, particularly at lower frequencies, such is into the megahertz and kilohertz range or lower.